Lemma 76.15.9. Let $S$ be a scheme. Let

be a fibre product diagram of algebraic spaces over $S$ with $h'$ formally unramified. Then $h$ is formally unramified and if $W \subset W'$ is the universal first order thickening of $W$ over $Y$, then $Z = X \times _ Y W \subset X \times _ Y W'$ is the universal first order thickening of $Z$ over $X$. In particular the canonical map $f^*\mathcal{C}_{W/Y} \to \mathcal{C}_{Z/X}$ of Lemma 76.15.8 is surjective.

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